On the entropy of processes generated by quasifactors

RÃ´mulo M. Vermersch

dynamical systems

On the entropy of processes generated by quasifactors

arXiv:2511.00891

summary

The paper proves that for a compact metric dynamical system with finite positive measure-theoretic entropy, every full‑support quasifactor of the invariant measure also has positive entropy.

Abstract

Given a measurable dynamical system $(X, X, I^¼, T)$ with $h_{I^} ¼ (T) < \infty$ , where $X$ is a compact metric space, $X$ is the Borel $I ¨ $ -algebra on $X$ , $I^¼$ is a $T$ -invariant Borel probability measure and $T$ is a homeomorphism acting on $X$ we show that, if $h_{I^} ¼ (T) > 0$ , then $h_{I^¼} (T) > 0$ for every quasifactor $I^¼$ of $I^¼$ having full-support.

Topics & keywords

#entropy #quasifactors #measure-theoretic dynamics #invariant measures #compact metric spacesmeasure-theoretic entropyquasifactorfull supporthomeomorphismBorel probability measure